System of Time-Temperature Integrators

ABSTRACT

Time-temperature integrators (TTIs) are useful for providing a means to monitor safety of fresh foods, particularly foods packaged in reduced-oxygen environments. TTIs of the present invention utilize Arrhenius-type curves to offer safety margins that satisfy regulator and shelf-life requirements. One method of using TTIs of the present invention involves using duel TTIs, one as a reference and one as a safety.

CROSS REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of U.S. Provisional Application60/537,103, filed on Jan. 16, 2004, which is hereby incorporated byreference in its entirety, including all tables, references and figures.

This invention was made with government support under National ScienceFoundation grant number 9316887. The government has certain rights inthe invention.

BACKGROUND OF THE INVENTION

Reduced-oxygen packaging (ROP) of fresh foods offers at least 2 majorbenefits: (1) improved production, handling and distribution efficiencyand (2) shelf-life extension. Reduced-oxygen packaging is usuallyperformed with vacuum packaging (VP) or modified atmosphere packaging(MAP). Vacuum packaging involves removal of gas from a package, whereasMAP involves altering the gaseous composition of the atmosphere within apackage in a prescribed manner.

Introduction of VP for distribution of chilled beef is recognized as oneof the most important developments in meat handling during the 20thcentury Robertson 1993). Prior to this innovation, large portions ofanimal carcasses were transported to local butchering operations. Today,slaughter and gross portioning are performed in well controlled,centralized facilities. Unused carcass parts are removed prior todistribution. Beef products are now internationally available asstandardized, easily handled, vacuum-packaged units known as “boxedbeef”.

Once beef is vacuum packaged, the residual gaseous environment becomesdeficient in oxygen and enriched in CO₂. This type of environment hasbeen shown to be beneficial for two reasons: (1) growth of aerobicmicroorganisms responsible for spoilage is reduced and (2) CO₂ dissolvesin moist foods and establishes equilibrium with carbonic acid, whichreduces pH (increase acidity) and further inhibits microbial growth.Ample research has shown that many other types of fresh foods can alsobenefit from ROP including poultry and seafood, as well as respiringproducts such as fruits and vegetables.

Botulism is a serious paralytic disease caused by eating foods thatcontain a potent nerve toxin produced by the bacterium Clostridiumbotulinum. Historically, botulism was associated with canned foods thatwere either damaged or insufficiently sterilized. Recent trends towardROP of fresh foods are creating more avenues of risk for this disease.Reduced-oxygen packaging of fresh or minimally processed seafood may beone of the most significant risks facing industry and consumers since ithas been shown that toxin may be present prior to obvious spoilage (FDA2001). This danger is compounded by the fact that seafood is oftencooked less severely than other foods. Therefore, solving safety issuesrelated ROP of fresh seafood may pave the way for application of ROPtechnologies to many types of foods.

Seafood consumption in the United States has been steadily increasingsince the mid-1950s (Gerdes and Valdez 1991). Data from the FloridaDepartment of Environmental Protection-Marine Fisheries values annuallanded seafood in Florida at over $200 million. Demand for fresh seafoodcontinues to grow, while our ability to preserve product quality remainslimited. Although studies have shown that MAP may be capable ofextending the shelf-life of fresh fish (Hong and others 1996), its useis limited due to the danger of pathogenic bacteria causing toxicityprior to obvious spoilage. This is due to two diametrically opposedroles of spoilage bacteria. On one hand, it is desired to reducespoilage organisms to preserve quality. On the other, the Food and DrugAdministration (FDA) is concerned that if spoilage organisms are reducedor eliminated, products may become toxic prior to onset of noticeablespoilage.

Spoilage begins as soon as fish die. Normal defense mechanisms seize,and a series of changes caused by bacteria, enzymes and chemical actionallow spoilage to begin. Bacteria are believed to be the most importantcause of seafood spoilage (Price 1990). In addition to bacteria, oxygenin the atmosphere can attack fats causing rancidity, off odors andoff-flavors. This is especially important in fatty fish such as salmonand mackerel. Evidence of oxidative damage has been noted whileattempting to preserve fish on deep-water fishing vessels, where it wasfound that gills of ice-immersed fish exposed to “air pockets” turnedbrown, while unexposed gills remained red (Scarlatti 1965). Undertraditional conditions, aerobic bacteria tend to be the major cause ofspoilage in fish. Therefore, researchers have been attempting to extendthe shelf life of fresh fish by reducing exposure to oxygen via modifiedatmosphere packaging. Although it has been shown that spoilage can bedelayed by removing oxygen (Stammen and others 1990; Penney and others1994; Hong and others 1996); doing so introduces the danger thatapparently unspoiled fish may contain C. botulinum toxin. For thisreason, the FDA has instituted strict guidelines for the use of ROP forseafood. It is likely that this issue is also central to FDA'sreluctance to approve irradiation as a means to extend the shelf life offresh seafood (Federal Register 1990).

C. botulinum forms toxin more rapidly at higher temperatures than atlower temperatures (Table 1). The minimum temperature for growth of C.botulinum type E and nonproteolytic type B and F is believed to bearound 3.3° C. (38° F.). As shelf life of refrigerated foods increases,more time is available for C. botulinum growth and toxin formation. Asstorage temperatures increase, time required for toxin formationdecreases. The Food and Drug Administration encourages industry toexpect that proper refrigeration temperatures will not be maintainedduring storage, distribution, display or consumer handling ofrefrigerated foods. Surveys of retail display cases indicate thattemperatures of 7 to 10° C. (45 to 50° F.) are not uncommon (FDA 2001).Surveys of home refrigerators indicate that temperatures can exceed 10°C. (50° F.) (FDA 2001).

To assist in identifying potential hazards in food processing anddistribution process, FDA offers three factors that are conducive totoxin formation, two of which are related to the packaging (FDA 1998).

(1) Vacuum packaging or modified atmosphere packaging. Because most ofthese packaging methods exclude or reduce the amount of oxygen in thepackage, conditions may be favorable for C. botulinum growth and toxinformation; (2) packaging in hermetically sealed containers (such asdouble seamed cans, glass jars with sealed lids, heat sealed plasticcontainers) or packing in oil. These and similar processing/packagingtechniques prevent the entry of oxygen into the container. Any oxygenpresent at the time of packaging may be rapidly depleted by the activityof spoilage bacteria, resulting in a reduced-oxygen environment that isfavorable for C. botulinum growth and toxin formation.

Evidence of the danger of toxigenesis prior to observable spoilage atmildly abusive temperatures has been demonstrated (Post and others1985). Table 1 summarizes data reported by Reddy and others (1996,1997a, 1997b). These studies demonstrate the potential of MAP to extendacceptable shelf life, and the remote possibility of toxigenesis prioror coincident to obvious spoilage at mildly abusive temperatures.

TABLE 1 Data demonstrating potential for toxigenesis prior or coincidentto observable spoilage under mildly abusive temperature conditions.Temperature (° C.) 4 8 16 Spoilage Toxic Spoilage Toxic Spoilage Toxic(d) (d) (d) (d) (d) (d) Reddy and Tilapia Air 10 >47 6 20 3 4 others1996 75% CO₂/25% N₂ 80 >90 17 40 4 4 Vacuum 47 >90 10 17 3 3 Reddy andSalmon Air 24 to 27 >66 13 to 17 17 4 4 others 75% CO₂/25% N₂ 55 to62 >80 20 to 24 24 5 to 6 4 1997a Vacuum 34 to 38 >66  6 to 10 10 3 3Reddy and Catfish Air 13 >54 6 9 3 3 others 75% CO₂/25% N₂ 38 to 40 >7513 18 4 4 1997b Vacuum 20 to 24 46 6 6 3 3

Recently, Skinner and Larkin (1998) proposed an empirical relationshipthat provides a conservative prediction for the time required to observeC. botulinum toxin as a function of temperature. The Skinner and Larkinrelationship is a simplified and more conservative version of anexpression proposed by Baker and Gerigeoris (1990). The Skinner andLarkin relationship follows:

Log(L)=0.65−0.0525T+2.74/T  (1)

where L is the “lag time” or “time-to-toxigenesis” in d, and T is thetemperature in degrees Celsius. FIG. 1 shows a plot of the Skinner andLarkin curve. The Skinner and Larkin curve represents an empiricalborder around virtually all known conditions where growth of C.botulinum have been shown to occur. Therefore, the 2 regions shown inFIG. 1 represent the best understanding of conditions where C. botulinumcan and cannot grow.

It is well known that properties of natural and synthetic materialschange over time. In the case of foods, particularly refrigerated freshfoods, such changes are generally-undesirable, and reflect deteriorationof food quality and/or safety. It is also generally recognized that therate at which such changes occur vary with temperature. For the case oftoxin liberation by C. botulinum, Eq. 1 describes this temperaturesensitivity.

Germination of bacterial spores and the growth of the bacteria arehighly complex processes that depend on many factors (Sarathehandren andothers 1977). Due to the conservative nature of the Skinner and Larkinrelationship, such complex issues may be ignored in order to focus onone critical parameter, namely temperature.

Temperature is often cited as the most important factor affecting foodsafety and quality (Shimoni and others 2001). Since changes in foodsoften involve highly complex and poorly understood mechanisms,time-temperature integrators (TTIs) are designed using fairly simplephysical and/or chemical systems that have well understood temperaturesensitivity characteristics. Therefore, the purpose of a TTI system isto relate a readily observable change in the TTI to changes that are notas readily determined in foods. Specifically, TTIs designed to ensuresafety of fresh ROP seafood should allow an observer to relate TTIreadings to the Skinner and Larkin (1998) relationship (Eq. 1).

Commercial TTI vendors often provide “endpoint” data to describe TTIperformance. For example, Cox Technologies (Belmont, N.C., U.S.A.)recommends its VITSAB M2-10 for seafood. The designation “M2-10”suggests that the TTI should expire in 10 days at 2° C. Additionaltime-temperature performance combinations for the M2-10, as provided bythe company, compared with Eq. 1 are shown in Table 2.

TABLE 2 Comparison of VITSAB M2-10 expiration to Skinner and Larkinrelationship (Eq. 1). All values in days. Temperature (° C.) 0 1 2 3 4 56 7 8 9 10 M2-10 14.0 12.0 10.0 8.4 7.0 6.0 5.0 4.0 3.5 2.5 2.0 Skinnerand Larkin 2175.2 82.2 25.5 13.3 8.6 6.2 4.7 3.7 3.0 2.5 (Eq. 1)

Other approaches to TTI approximations and techniques to manufacture TTIdevices can be found in U.S. Pat. Nos. 5,667,303; 6,244,208; 6,435,128;and 6,614,728. These devices all monitor the cumulative temperatureexposure of a product or package to temperature.

Interestingly, information about the path between endpoints is nottypically provided. In other words, the current approach to TTI designfocuses solely on matching temperature sensitivity of the TTI to theunderlying process. Although this approach may be theoretically sound,it may lead to technically correct, yet poorly behaved TTIs that aredifficult to interpret subjectively.

The rate at which the TTI readings change with time can often be modeledwith well known kinetic expressions. For instance, the rate of change ofan observable TTI parameter, A, can be said to follow the general form:

$\begin{matrix}{{\pm \frac{A}{t}} = {kA}^{n}} & (2)\end{matrix}$

where k is often referred to as the reaction rate constant, and n is thereaction order. In highly complex systems such as foods, global changesoften follow pseudo-zero (n=0) or pseudo-first order (n=1) kinetics.

First-order kinetic behavior is often observed in nature. Well-knownexamples are radioactive decay, and exponential-phase bacterial growth.In such cases it is easy to see that the rate of change of A at anygiven time is proportional to the magnitude of A at that time:

$\begin{matrix}{{\pm \frac{A}{t}} = {kA}} & (3)\end{matrix}$

Conversely, zero-order behavior is not observed in nature as often.However pseudo-zero order behavior is observed in systems where apotentially limiting component is available in sufficiently excessiveamounts that the limitation becomes insignificant. Such behavior isobserved in catalyzed reactions in which catalyst concentration isabundant. For the zero-order case, the rate of change is constant:

$\begin{matrix}{{\pm \frac{A}{t}} = k} & (4)\end{matrix}$

Solving Eq. 3 and 4 provides relationships that can be used to describethe behavior of zero and first order TTIs between the specified times.

$\begin{matrix}\underset{\_}{n = 0} & \underset{\_}{n = 1} \\{{\pm \frac{A}{t}} = k} & {\frac{A}{t} = {{\pm {kA}}\mspace{11mu} \left( {{5a_{0}},{5a_{1}}} \right)}} \\{{\pm {\int_{A_{0}}^{A}{A}}} = {k{\int_{0}^{r}{t}}}} & {{\int_{A_{0}}^{A}{A}} = {k{\int_{0}^{r}{{\pm {t}}\mspace{14mu} \left( {{5b_{0}},{5b_{1}}} \right)}}}} \\{A = {A_{0} \pm {kt}}} & {A = {A_{0}{^{\pm {kt}}\left( {{5c_{0}},{5c_{1}}} \right)}}}\end{matrix}$

Equations 5c₀ and 5c₁ represent the response paths that zero and firstorder TTIs would provide. If it is assumed that the response of theVITSAB M2-10 follows zero order kinetics, then the reaction rate at 2°C. would be:

$\begin{matrix}{k = {\frac{A_{0}}{t} = {\frac{{100\%} - {0\%}}{10\mspace{14mu} {days}} = {{10\mspace{14mu} {days}} = {10\% \mspace{14mu} {per}\mspace{14mu} d}}}}} & (6)\end{matrix}$

where 100% and 0% refer to the amount of observable response remainingat the beginning and end of the 10 days, respectively. In other words,when the M2-10 is stored at 2° C., an observer could expect to see asimilar amount of response during each of the 10 days until expiration.In this case that amount would be 10% of the total response per day.

If the M2-10 follows first-order kinetics, then we would need to knowmore about the state of the TTI when it expires in order to be able todetermine the reaction rate constant, k, and to predict the path of theresponse. This is due to the fact that first-order behaviorasymptotically approaches the expiration point and never actuallyachieves complete expiration. For this reason, the end of the TTI'sresponse must be defined as a fraction of the TTI's total response,A/A0. With this additional information, the reaction rate constant maybe calculated as follows:

$\begin{matrix}{k = \frac{\ln \left( {A/A_{0}} \right)}{t}} & (7)\end{matrix}$

FIG. 2 shows expected response paths for the VITSAB M2-10 stored at 2°C., assuming both zero and 1st-order kinetics. For the first order case,several possible endpoint specifications are shown.

Note that all of the curves in FIG. 2 satisfy the M2-10 specification,in that they all reach the specified endpoint in 10 days (240 h) at 2°C. Although each of these paths would provide a conservative responserelative to the Skinner and Larkin formula for C. botulinum, thedifferences in the paths raise some practical concerns with regard toactual use. To illustrate, consider the first order TTI for which theend of response is A/A₀=0.01. Under constant temperature storage at 2°C., an observer would note a fairly rapid response during the first twoto three days, but would then see very small changes until expiration.Conversely, for the first order response when the endpoint A/A₀=0.7, therate of change would appear to be fairly slow, but consistent. For thezero-order case, the response would appear constant throughout, asexpected.

Upon comparing the zero-order and first-order A/A₀=0.7 response curves,it is clear that, while both offer consistent changes over time, theoverall response of a corresponding first-order TTI would be much moresubtle than the zero-order TTI. Therefore, given a choice, thezero-order behavior should be preferable.

As shown, an appropriate assumption of reaction order, n, allowsdetermination of the associated reaction rate constant, k, from endpointspecifications. The Arrhenius relationship (Eq. 8) often describes how kvaries with temperature:

$\begin{matrix}{k = {k_{0}{e\left( \frac{- {Ea}}{RT} \right)}}} & (8)\end{matrix}$

where E_(a) is the activation energy; R is the ideal gas law constant; Tis absolute temperature; k₀ is a constant. Generally, reaction rateconstants increase with temperature. The sensitivity of the rateconstant to temperature is governed by the magnitude of E_(a). For twodifferent reactions or, in this case TTIs, with different E_(a) values,Eq. 8 dictates that the reaction rate constant with the greateractivation energy will change by a greater amount for a given change intemperature.

Arrhenius parameters, k₀ and E_(a), are typically determined from a plotof ln(k) versus inverse absolute temperature. Equation 9 shows that whensuch a plot produces a line, the slope is equal to −Ea/R and theintercept is ln(k₀).

$\begin{matrix}{{\ln (k)} = {{\ln \left( k_{0} \right)} - {\frac{E_{a}}{R}\left( \frac{1}{T_{absolute}} \right)}}} & (9)\end{matrix}$

Since it is likely that most commercial TTIs demonstrate Arrheniustemperature sensitivity, it may be useful to transform the empiricalSkinner and Larkin (1998) formula (Eq. 1) into a corresponding Arrheniusrelationship, so that appropriate comparisons can be made. As previouslynoted, the reaction order, n, must be assumed in order to convertSkinner and Larkin (1998) lag-times into reaction rate constants.

Physically, the end of the Skinner and Larkin lag-time, L, correspondsto germination of C. botulinum spores, growth of bacteria and liberationof toxin. During the lagtime, there are no convenient measurements thatcan be made to estimate the amount of lag-time already consumed orremaining. The critical and practical aspect is that there must be anabsolute understanding that once the safe lag-time is depleted, the ROPfood is unconditionally surrendered. In other words, the endpoint isclear, definite, and absolute; an inherent characteristic of zero orderkinetics. Moreover, the endpoint is not an arbitrary point on anasymptotic curve, an inherent characteristic of first order kinetics.Therefore, it should be sufficient and conservative to assume thatconsumption of lag-time follows the most direct path, which is definedby zero-order kinetics. However, this does not mean that the approachdescribed here is restricted to TTIs with zero-order kinetic responses.The approach can be applied equally well to TTIs with first-order, orother types of kinetic responses. However, given the physical nature ofthe consumption of lag-time, it is suggested that TTIs offeringzero-order kinetics are preferable. Therefore, development of theapproach below focuses on the case of zero-order kinetics. Using thezero-order kinetic assumption, Skinner and Larkin (1998) reaction rateconstants may be calculated directly from lagtimes calculated in amanner similar to that described by Eq. 6:

$\begin{matrix}{{k(T)} = \frac{100}{L(T)}} & (10)\end{matrix}$

FIG. 3 shows the Skinner and Larkin (1998) formula in Arrhenius form,assuming zero order kinetics. This curve shall be referred to asS&L-Arrhenius curve.

Prior to applying FIG. 3 in the development of methodology appropriatefor TTIs, it is important to be able to interpret FIG. 3 properly. SinceFIG. 3 was created with the assumption of zero-order kinetics, Eq. 5a₀dictates that the reaction rate constant, k, is also equivalent to therate of loss of lagtime. Therefore, when comparing rates of change ofzero-order indicator systems to that of the modified S&L-Arrhenius curvein FIG. 3, points above the curve represent TTI changes that are fasterthan consumption of lag-time, while those below represent TTI changesthat are slower than consumption of lag time. Since the objective of anyTTI is to provide an accurate, yet conservative indication of theconsumption of lagtime (or other corresponding process), it isappropriate for zero-order TTI response curves to approach theS&L-Arrhenius curve from above. In other words, it is desirable to be asclose to the S&L-Arrhenius curve as possible, but never below the curve.

Time-temperature integrator technology offers a promising approach tomonitoring product quality and safety. However, a greater understandingof TTI performance attributes is required before confidence in theirability to ensure product safety is achieved. Specifically, proceduresneed to be established that define how TTIs are to be read, as well ashow such readings are to be used. Once such procedures are established,studies need to establish appropriate statistics related to expectedperformance. These statistics will allow development of limits that willdefine an appropriate proximity for mean TTI performance to theestablished border of safety.

Additionally, it is important to understand how external influencesmight affect TTI performance. Such influences might include (1)handling, storage and shelf-life of the TTIs, (2) location of a TTI on apackage, (3) weight of other packages on a TTI, (4) effects of differentforms of light in TTIs, and (5) brief exposures of TTIs to environmentextremes before and during use.

The time required for C. botulinum spores to germinate, grow andliberate toxin is often reported as a “lag time” or “time totoxigenesis” (Skinner and Larkin 1998). It can be useful to considerthis period of time as a consumable resource with specific initial andending conditions, namely 100% of lag time remaining and 0% of lag timeremaining, respectively. The actual path taken between these 2 points isnot well understood, but it is not particularly important since theunderlying food is safe at all conditions between these 2 points. At thevery least, it is conservative to assume that the path taken is astraight line under constant thermal conditions. This considerationprovides a useful, but not restrictive performance target for timetemperature integrator devices. The concept of lag-time is not limitedto C. botulinum spores growing in fish but can be used to approximatethe lag time of any pathogenic microorganism, for example, but notlimited to, C. Botulinum, enterotoxigenic E. coli, salmonellae sp,exotoxin shigalla dysenteriae, staphylococcus aureus, enterotoxinKlebsiella pneumoniae, Bacillus cereus, Vibrio parahaemolyticus, Vibriocholerae, Campylobacter jejuni, Campylobacter jejuni, Yersiniaenterocolitica, Exotoxin Pseudomonas aeruginosa, C. perfringens,Versinia enterocolitica, and Listeria monocytogenes.

The skilled artisan would also understand that lag time can also beapplied to sprouting in root vegetables and ripening of live foods likefruits. Lag time can also be used to indicate spoiling. The additionalconsideration of the inherent shelf-life of a particular fresh foodpackaged in a reduced-oxygen environment, provides a safe and practicalproduct-specific TTI performance specification.

BRIEF SUMMARY OF THE INVENTION

The present invention comprises a system of time-temperature integrators(TTI) to ensure food product safety, particularly reduced oxygenpackaged fresh fish A first TTI predicts when the product lagime isdepleted. A second TTI is useful as a reference indicator to analyzeinefficiencies in supply chain temperature. The reaction mechanisms thatdrive the indicator are both zero order reactions. The first TTI isdesigned to performed according to curve E of FIG. 6, which is apredictive model for the depletion of lagtime. The second TTI isdesigned to perform more sluggishly to changes in temperature fortemperatures below some predetermined critical temperature and moresensitively for temperatures above the critical temperature.

The method of using the TTIs comprises observing the rates of change inthe indicator mechanism and analyzing the changes using a color chart ora hand held spectrometer. If the change is greater in the first TTI, thefood has been consistently exposed to desirable temperatures. If thechange is greater in the second TTI, the food product has been exposedto undesirable temperatures although the product may be safe to eat.

BRIEF DESCRIPTION OF THE FIGURES

FIG. 1—The Skinner and Larkin (1998) relationship (Eq. 1).

FIG. 2—Possible response paths of the Vitsab® M2-10 TTI under constanttemperature storage at 2° C., assuming zero and first order kinetics.

FIG. 3—Arrhenius plot of Skinner and Larkin (1998) formula assuming Zeroorder kinetics.

FIG. 4—Depiction of extremes for specifying zero-order TTI performance.

FIG. 5—Arbitrary approaches for compromising between extremes shown inFIG. 4.

FIG. 6—Proposed method for specifying zero-order TTI performance.

FIG. 7—Desired tangent line that contains P1 must either be selectedfrom more than one possible solution, or the search for P2 must beconstrained to the region of particular physical interest.

FIG. 8—Simulation of TTI performance (P1 specified by 18-d shelf-life at1° C.) versus Skinner & Larkin (1998) lag-time under abusivedistribution conditions.

FIG. 9—Simulation of TTI performance (P1 specified by 18-d shelf-life at1° C.) versus Skinner & Larkin (1998) lag-time under abusive dailytemperature cycles.

FIG. 10—Duel indicator system at important temperatures.

FIG. 11—Response patterns for a safety TTI and a reference TTI relativeto actual temperature.

DETAILED DISCLOSURE OF THE INVENTION

The manner in which the S&L-Arrhenius curve is used to design and/orspecify TTI performance depends on the nature of the TTI response.Ideally, one would prefer TTIs to behave identically to theS&L-Arrhenius curve. However, this may be difficult to achieve for anygiven indicator system. A viable alternative could include TTIs withzero-order response characteristics, and an Arrhenius curve that is asclose to the S&L-Arrhenius curve as possible, but without crossing belowthe S&L-Arrhenius curve. FIG. 4 presents two such Arrhenius curves(lines A and B) that represent the extremes of all possible curves thatsatisfy this requirement.

Although zero-order TTIs offering the performance depicted by lines Aand B (FIG. 4) would provide conservative responses relative to theSkinner and Larkin (1998) formula, it is worth noting the practicalimplications of these extreme cases. Before doing so, it is worth notingthree points regarding Arrhenius plots. First, increasing values ofln(k) represent increasing values of the reaction rate constant, k.Second, for the case of zero-order kinetics, the rate constant is equalto the reaction rate. Third, the abscissa of an Arrhenius plot is“inverse absolute temperature,” therefore, temperature decreases towardthe right and increases to the left.

Consider a TTI with temperature sensitivity described by curve B (TTI-B)in FIG. 4. This TTI closely matches the S&L-Arrhenius curve at lowtemperatures, but becomes increasingly faster (more conservative) astemperature increases. For the case of ROP seafood, TTI-B would performwell for product distributed and stored under properly controlledtemperatures. However, the TTIs would quickly expire under briefexposure to even moderate temperatures. In most cases of slight tomoderate temperature abuse, TTI-B would expire well before theunderlying products would actually become unsafe to consume. The resultbeing that even insignificant lapses in temperature control duringdistribution or storage would likely result in significant waste ofotherwise safe product.

Now consider TTI-A in FIG. 4. Time-temperature integrator-A becomesincreasingly conservative (faster) than consumption of lag time at lowtemperatures. For the case of ROP seafood, TTI-A will expire well beforetoxigenesis even when product temperature is perfectly controlledthroughout distribution and storage. Time-temperature integrators-Awould become increasingly accurate as thermally abusive conditionsbecome more severe.

FIG. 5 depicts one seemingly straightforward, yet arbitrary andpotentially dangerous attempt to compromise between the extremes (curveC), as well as a safer alternative (curve D).

Curve C (FIG. 5), can be created via linear regression of either theentire S&L-Arrhenius curve or some arbitrarily selected sub-region.Since it is the purpose of any regression to find the path of leasterror through a set of data, it should be expected that the resultingline will pass above and below the elected data points (curve C, FIG.5). Clearly, a zero-order TTI with curve C performance would not beconservative within the temperature range where the curve falls belowthe S&L-Arrhenius curve.

The dangerous region of curve C can be avoided by applying an additiveoffset of an amount equal to the greatest difference between curve C andthe S&L-Arrhenius curve, resulting in curve D (FIG. 5). Curve Drepresents a safe and conservative performance specification for azero-order TTI, however, it retains the arbitrary nature of curve C,because it depends on the particular range of data used in theregression.

FIG. 6 represents a more specific approach that is conservative,practical and not arbitrary. Curve E (FIG. 6) is constructed from twopoints, one that is relevant to the product, and another from theS&L-Arrhenius curve. The result is a curve that provides (1) anappropriate response when temperature control is excellent, (2) thesmallest possible excessive response as temperature increases, while (3)ensuring a safe and conservative response under all temperatures. Theproduct-related point, P1, is defined by the actual shelf life realizedunder ideal conditions. In other words, P1 represents the maximumachievable shelf-life of the product. For example, if 20 days ofshelf-life are achieved at 0° C., then P1 is defined on the plot as{1/273.15, ln([100%/−0%]/20 days)}. The second point, P2, is defined bythe tangent to the S&L-Arrhenius curve that contains P1. Curve E (FIG.6) offers a practical compromise between realistic shelf life and;unnecessary waste of otherwise safe product. A zero-order TTI with curveE performance (TTI-E) provides the appropriate shelf-life at lowtemperature, accurate safety indications at moderate temperatures, andconservative indications under increasingly abusive conditions.

Point P2 can be found using many widely available tools such as theSolver feature of Microsoft Excel. However, it is important to note thatit is possible to find more than one mathematical solution. Therefore,it is necessary to either discard undesirable solutions, or to constrainthe search to a region appropriate to the physical nature of theproblem. FIG. 7 shows the behavior of the Skinner & Larkin Arrheniuscurve over a wider range of temperature values. For the case of unfrozenROP seafood, identifying the proper solution or constraining the searchfor the desired solution is not too difficult, because P1 will likely bedefined by temperatures approaching 0° C. (1/273.15) from the positiveside (fresh fish, by definition, is unfrozen). Therefore, the desiredsolution is likely at a temperature somewhat above that of P1. For anumber of practical situations, constraining the search for P2 totemperatures above 1° C. has proven to be sufficient. The slope of thetangent to the S&L-Arrhenius curve is defined by the derivative of thiscurve. The equation for the slope of the tangent line is

$\begin{matrix}{{f^{\prime}(x)} = {- {{\ln (10)}\left\lbrack {\frac{0.0525}{x^{2}} + \frac{2.74}{{x^{2}\left( {\frac{1}{x^{2}} - 273.15} \right)}^{2}}} \right\rbrack}}} & (11)\end{matrix}$

where x is inverse absolute temperature (1/T_(abs)).

FIGS. 8 and 9 show predicted response curves for a zero-order TTIconstructed in a manner described by curve E (FIG. 6). For this case,point P1 was defined by a product that provides 18 d of shelf life at 1°C. The tangent to the S&L-Arrhenius curve that contains P1 was found tooccur at 8.0° C. The line passing through these points provides thedesired Arrhenius specification for the desired zero-order TTI:

$\begin{matrix}{{\ln (k)} = {64.86 - \frac{17311}{T_{absolute}}}} & (12)\end{matrix}$

Equations 12 and 1 were used to simulate response characteristics underabusive dynamic thermal conditions. In each case, the dynamic thermalcondition was generated using the following sine-squared function:

$\begin{matrix}{{T(t)} = {T_{Base} + {A\; {\sin^{2}\left( \frac{2\pi \; t}{P} \right)}}}} & (13)\end{matrix}$

where T is temperature in ° C., T_(base) is a base or minimumtemperature of the cycle, A is the amplitude of the cycle (maximumtemperature reached in a cycle is T_(base)+A), P is the period of thecycle, and t is time in h. Response values were calculated using a1-hour time interval. Temperature values equal to 10% above the meantemperature for each interval was used for kinetic response calculations(Welt and others 1997).

FIG. 8 depicts a situation in which product is manufactured and packagedunder controlled conditions of 1° C., then transits a poorly controlleddistribution chain, but then returns to controlled conditions forstorage and/or sale (T_(base)=1° C., A=8° C., P=500 h).

FIG. 9 depicts a daily fluctuation of temperature between 1 and 9° C.(T_(base)=1 C, A=8° C., P=48 h).

As expected, FIGS. 8 and 9 demonstrate that a zero-order TTI engineeredto perform in accordance with Eq. 12 would provide a safe andconservative indication. Under any possible conditions, the TTI isexpected to expire prior to the conservative prediction of toxigenesisprovided by the Skinner and Larkin (1998) formula (Eq. 1).

One embodiment of the present invention comprises a system of TTIsuseful for monitoring food safety. Advantageously, a system of TTIsallows the user to monitor the temperature changes during the supplychain history in addition to providing information to the depletion oflag time. Preferably, the system comprises two TTIs. Preferably, theTTIs indicate food safety information using changes of color. Thechanges of color can be analyzed by use of a handheld spectrometer or byobservation and comparison with a color chart. In yet anotherembodiment, the TTIs are digital and perform calculations for theapproximation of lag time. The results are then displayed and/ortransmitted to the appropriate personal.

The first TTI, or safety TTI, is designed, utilizing techniques known inthe arts, with a larger activation energy for the reaction driving theindicator mechanism. The reaction can be, for example, an enzyme-lipidreaction or a viscoelastic material designed to decay according toEquation 12. In addition to showing the rate of decay of the lagtime,the first TTI is designed to indicate complete depletion of lagtime. Atthis indication, the food product is no longer safe to eat.

In order to supply more information about the food supply chain, thefirst TTI can be used in conjunction with a second TTI. The second TTI,or the reference TTI, is preferably manufactured to perform a zero orderdecay with a different activation energy, or temperature sensitivities,than the reaction mechanism of the first TTI; however, the inventionalso applies to non-zero reaction orders as well. The reaction drivingthe second TTI preferably has a smaller activation energy relative tothe first TTI, and the second TTI is not as sensitive to temperature asthe first TTI. Optionally, the second TTI can be designed with a largeractivation energy, resulting in opposite behavior than is described;however, a second TTI with smaller activation energy is preferred andused for description. The reaction curve of the second preferred TTIcrosses the reaction curve of the first TTI at a critical temperatureselected for the food product by the operators (see, for example FIG.10). Storage at temperatures greater than the critical temperatureresults in larger decay in the second TTI relative to the first TTI.

Another aspect of the present invention is a method of using a dual TTIsystem to monitor food safety. The method comprises comparing changes inthe indicator systems of a first TTI to a second TTI, where the TTIs areconstructed using the reaction design data of the present invention, andthe second TTI, preferably, has a smaller activation energy, or adifferent temperature sensitivity, than the first TTI. For the samechange in temperature, the first (safety) TTI changes color more quicklywhen the temperatures are lower than the critical temperature. Fortemperatures greater than the critical temperature, the color changesmore quickly in the second (reference) TTI. Optionally, the second TTIhas a larger activation energy than the first TI, which results in theopposite behavior. In other specific embodiments, the rates of changeare displayed digitally, by variable indications against a fixed scaleor any combination of the foregoing.

A method of the present invention utilized these temperature dependentqualities of the TTIs to develop a food safety inquiry. A method,wherein the rate of change is indicated by changes in color, comprisesobserving the change of color of the first TTI, observing the change ofcolor of the second TTI, and comparing the changes. For ease ininterpretation, a color chart showing possible changes in color or ahand-held spectrometer can be used to determine precisely the change incolor

If the rate of change of color of the first (safety) TTI is greater thanthe change of color in the second (reference) TTI, then the food productwas exposed to temperatures greater than the critical temperature(T_(c)) and the food supply chain should be investigated. If the rate ofchange of color is equal in both TTIs, then the food product was eitherexposed to temperatures consistently equal to the T_(c) or the productexperienced offsetting higher and lower thermal conditions. If the rateof change of the first (safety) TTI is greater than the rate of changeof the second (reference) TTI, then the product was handled well and thethermal history was mostly below the critical temperature. These typesof response patterns are illustrated in FIG. 11.

All patents, patent applications, provisional applications, andpublications referred to or cited herein are incorporated by referencein their entirety, including all figures and tables, to the extent theyare not inconsistent with the explicit teachings of this specification.

REFERENCES

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1. An improved time temperature integrator system comprising timetemperature integrators comprising a reaction rate mechanism having areaction rate constant (k); wherein the reaction rate mechanism exhibitstemperature sensitivity; wherein the improvement comprises a reactionrate mechanism that exhibits zero-order decay when exposed to atemperature, measured in Kelvin, according to the equation$^{\lbrack{64.86 - \frac{17311}{{Temp}{(K)}}}\rbrack}.$
 2. An improvedfresh food and perishable products monitoring system comprising timetemperature integrators comprising a reaction rate mechanism having areaction rate constant (k); wherein the reaction rate mechanism exhibitstemperature sensitivity; wherein the reaction rate mechanism decays whenexposed to temperature; wherein the improvement comprises a reactionrate mechanism approximated by reaction kinetic schemes.
 3. The systemaccording to claim 2, wherein the reaction rate mechanism of a safetytime temperature integrator exhibits zero-order decay when exposed totemperature.
 4. The system according to claim 3, wherein the zero-orderdecay of the reaction rate mechanism of a safety time temperatureintegrator approximates depletion of lag time for pathogenicmicroorganisms.
 5. The system according to claim 4, wherein thepathogenic microorganism is selected from the group consisting of C.Botulinum, enterotoxigenic E. coli, salmonellae sp, exotoxin shigalladysenteriae, staphylococcus aureus, enterotoxin Klebsiella pneumoniae,Bacillus cereus, Vibrio parahaemolyticus, Vibrio cholerae, Campylobacterjejuni, Campylobacter jejuni, Yersinia enterocolitica, ExotoxinPseudomonas aeruginosa, C. perfringens, Versinia enterocolitica, andListeria monocytogenes.
 6. The system according to claim 3, wherein thereaction rate mechanism of a safety time temperature integratorapproximates depletion of lag time for temperature sensitive phenomenaselected from the group consisting of sprouting, ripening, and spoiling.7. The system according to claim 2, wherein a natural log of a referencetime temperature integrator's reaction rate constant is equivalent to anatural log of a safety temperature integrator's reaction rate constantat a critical temperature.
 8. The system according to claim 2, whereinthe decay of the reaction rate mechanism of a reference time temperatureintegrator indicates fluctuations in temperature.
 9. The systemaccording to claim 2, wherein a temperature sensitivity of a referencetime temperature integrator's reaction mechanism is different than atemperature sensitivity of a safety time temperature integrator'sreaction mechanism.
 10. The system according to claim 2, wherein thereaction kinetic scheme is zero-order.
 11. The system according to claim2, wherein the reaction kinetic scheme is first-order.
 12. The systemaccording to claim 2, wherein the reaction rate mechanism is a functionof temperature and is optionally estimated using fitting functions. 13.The system according to claim 12, wherein the reaction rate mechanism isestimated using fitting functions.
 14. The system according to claim 13,wherein the fitting function is a zero-order approximation.
 15. Thesystem according to claim 13, wherein the fitting function is afirst-order approximation.
 16. A method for monitoring perishability andsafety of fresh food or other perishable products, wherein the methodcomprises: a) providing a fresh food and perishable products monitoringsystem of claim 1; b) attaching the fresh food and perishable productsmonitoring system to a packaged fresh food or perishable product; c)observing the rates of change in each of the time temperatureintegrators; and d) comparing the rates of change in each of the timetemperature integrators.
 17. The method according to claim 16, whereinrate of change is indicated visually by a change of color; wherein theobserving step comprises measuring the change in color with aspectrometer or a color chart.
 18. The method according to claim 16,wherein the rate of change, extent of reaction of each of the timetemperature integrators or both the rate of change and extent ofreaction of each of the time temperature integrators is calculated. 19.The method according to claim 16, wherein the calculation performed byeach of the time temperature integrators is displayed digitally, as achange of color, by a variable indication against a fixed scale or anycombination thereof.
 20. The method according to claim 16, wherein theperishable product is a reduced-oxygen package of fresh fish. 21-22.(canceled)
 23. The method according to claim 18, wherein the calculationperformed by each of the time temperature integrators is displayeddigitally, as a change of color, by a variable indication against afixed scale or any combination thereof.